Echo cancelers are employed in modems in order to achieve full-duplex data communications. A number of different echo cancellation techniques have been employed in order to simplify the echo canceler structure and/or improve overall data communications. These prior techniques have employed echo cancelers at various positions in the receive path of the modem in attempting to improve over-all echo cancellation and, in particular, adaptation speed in synthesizing an echo. Indeed, it is desirable to have the echo canceler transversal filter impulse response rapidly converge to the impulse response of the echo path. To this end, the prior techniques "trained" the echo canceler during the so-called "half-duplex" operation of the modem. Modems are typically connected to a two-wire telephone line through a hybrid, i.e., 2-to-4-wire conversion, network, whose characteristics tend to change over time and, especially, because of temperature variations. Consequently, the echo canceler impulse response synthesis capability must be updated in order to track changes in the echo path impulse response characteristic. This is especially true in modems, employing the so-called PCM technique, i.e., pulse code modulation technique, which are embedded in personal computers, and particularly, laptop computers. In these and similar applications, because of the use of smaller so-called form factors in the circuitry, there are more rapid circuit characteristic changes caused by rapid temperature variations, which translate into faster impedance drift of the hybrid network. Thus, it is desirable to rapidly track variations in the echo path impulse response in order to enhance modem performance. This leads to a well known dichotomy of noise and rapid response. To achieve rapid response in synthesizing the echo path impulse response a large adaptation step size is desirable but causes noise which degrades data communication capability. To minimize noise a small adaptation step size is desirable but results in a slow convergence when synthesizing the echo path impulse response. This problem is acute in PCM modems because the values of PCM symbols vary significantly from one symbol to another and a very small adaptation step size is required in order to avoid adverse effects in the modem receiver performance. The small adaptation step size, of course, translates into too poor of a tracking capability for practical applications.